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Three contributions to Stein's method: Poincaré inequalities, discrete approximations, and density estimation
No full textLa méthode de Stein est un ensemble d'outils mathématiques introduits par Charles Stein dont l'idée centrale est de représenter des lois de probabilité par des opérateurs différentiels. Son objectif premier est d'établir des bornes supérieures sur des distances entre lois. Dans cette thèse, nous utilisons la méthode de Stein dans trois domaines différents issus de l'analyse, de la théorie des probabilités et des statistiques.Nous étudions d'abord l'inégalité de Poincaré associée à une loi unidimensionnelle. Nous obtenons une nouvelle version de la formule variationnelle de Chen-Wang et, en corollaire, des bornes supérieures et inférieures sur la constante de Poincaré exprimées en termes du noyau de Stein. En utilisant cette formule de façon itérée, nous parvenons à construire des suites d'intervalles imbriqués contenant la constante de Poincaré, des suites de fonctions convergeant vers cette constante, ainsi que des suites de fonctions convergeant vers les solutions du problème spectral correspondant. Nos résultats reposent sur les propriétés d'un opérateur pseudo-inverse de l'opérateur classique de Sturm-Liouville, notamment le fait que la constante de Poincaré est sa plus grande valeur propre. Nous illustrons nos méthodes sur une variété d'exemples :fonctionnelles de lois gaussiennes, lois beta, gamma, Subbotin et Weibull.Ensuite, nous introduisons une nouvelle version de la méthode de Stein par comparaison d'opérateurs, dans le cas spécifique où l'on cherche à borner la distance de Wasserstein-1 entre des lois continues et discrètes sur la droite réelle. Notre approche repose sur une nouvelle famille de dérivées discrètes pondérées. Nous proposons également de nouvelles bornes sur les dérivées des solutions des équations de Stein pour les variables aléatoires Pearson intégrées. Nous appliquons nos résultats à plusieurs exemples, y compris le théorème central limite, les modèles d'urnes de Pólya–Eggenberger, la distribution stationnaire du nombre de gènes dans le modèle de Moran, et la distribution stationnaire du système Erlang-C.Enfin, nous passons en revue la littérature concernant les applications de la méthode de Stein à l'estimation de densité. Nous considérons des estimateurs construits en minimisant une divergence de Stein entre la loi empirique des données et la loi du modèle. Dans le cas paramétrique, notre estimateur offre une alternative fiable à l'estimateur du maximum de vraisemblance, qui peut être difficile à calculer ou même inconsistant sous nos hypothèses. Dans le cas non paramétrique, nous explorons différentes façons de minimiser la divergence, notamment par la méthode de descente de gradient. Bien que de tels estimateurs existent déjà dans la littérature, nous en améliorons l'algorithme en sélectionnant la taille du pas de façon à optimiser la convergence.The Stein method is a set of mathematical tools introduced by Charles Stein, with the central idea of representing probability laws through differential operators. Its main objective is to establish upper bounds on distances between laws. In this thesis, we use the Stein method in three different fields: analysis, probability theory, and statistics.We first study the Poincaré inequality associated with a one-dimensional law. We obtain a new version of the Chen-Wang variational formula, and as a corollary, upper and lower bounds on the Poincaré constant expressed in terms of the Stein kernel. By using this formula iteratively, we construct sequences of nested intervals containing the Poincaré constant, sequences of functions converging to this constant, as well as sequences of functions converging to the solutions of the corresponding spectral problem. Our results rely on the properties of a pseudo-inverse operator of the classical Sturm-Liouville operator, notably the fact that the Poincaré constant is its largest eigenvalue. We illustrate our methods with a variety of examples: functionals of Gaussian laws, beta, gamma, Subbotin, and Weibull distributions.Next, we introduce a new version of the Stein method by comparing operators, in the specific case where we seek to bound the Wasserstein-1 distance between continuous and discrete laws on the real line. Our approach is based on a new family of weighted discrete derivatives. We also propose new bounds on the derivatives of the solutions of the Stein equations for integrated Pearson random variables. We apply our results to several examples, including the central limit theorem, Pólya–Eggenberger urn models, the stationary distribution of the number of genes in the Moran model, and the stationary distribution of the Erlang-C system.Finally, we review the literature on applications of the Stein method to density estimation. We consider estimators constructed by minimizing a Stein divergence between the empirical law of the data and the model's law. In the parametric case, our estimator provides a reliable alternative to the maximum likelihood estimator, which can be difficult to calculate or even inconsistent under our assumptions. In the non-parametric case, we explore different ways of minimizing the divergence, notably through the gradient descent method. While such estimators already exist in the literature, we improve the algorithm by selecting the step size to optimize convergence.Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe
Shifting trait coordination along a soil‐moisture‐nutrient gradient in tropical forests
No full textAbstract Soil nutrients and water availability are strong drivers of tropical tree species distribution across scales. However, the physiological mechanisms underlying environmental filtering along these gradients remain incompletely understood. Previous studies mostly focused on univariate variation in structural traits, but a more integrative approach combining multiple physiological traits is needed to fully portray species functional strategies. We measured nine leaf functional traits related to trees' resource capture and hydraulic strategies for 552 individuals belonging to 21 tropical tree species across an environmental gradient in Amazonian forests. Our sampling included generalist and specialist species from terra firme (TF) and seasonally flooded (SF) forests. We tested the influence of the topographic wetness index, a proxy for soil moisture and nutrient gradients, on each trait separately and on the trait integration through multivariate indices computed from the eigenvalues of a principal component analysis on the traits of the species. Finally, we evaluated intraspecific trait variability (ITV) for generalists and specialists by calculating the coefficient of variation for each trait. Results showed that (1) the environment had a greater influence on trait syndromes than single trait variation. Moreover, (2) SF specialist species expressed a stronger leaf trait coordination than TF specialist species. Furthermore, (3) the ability of generalist species to occupy a broader range of environments was not reflected by a larger ITV than specialist species but by the capacity to change trait coordination across environments. Our work highlights the need to investigate functional strategies as multidimensional syndromes in physiological trait space to fully understand and predict species distribution along environmental gradients. Read the free Plain Language Summary for this article on the Journal blog.info:eu-repo/semantics/publishe
De-pioneering the history of architecture: from Simone Guillissen-Hoa (1916-1996) to her constellations
No full textCritique of the pioneer canonRecent research and publications that articulate the history of architecture and gender describe figures qualified as pioneers. The method adopted establishes lists of portraits of the first women to study - graduate - build - photograph - and sell (delete as appropriate) in a chronology "outside of the world" [“hors du monde”]. These narrative methodologies and language elements outline "a new canon, that of women artists’ art history" - from which the field of architecture is not exempt - "just as excluding as the one it seeks to denounce". Indeed, using the analytical and semantic field of the pioneer does offer a narrative, a seemingly new and different "feminine" history, but it is incomplete because always disconnected from an historical genealogy that is still under construction. This truncated posterity highlights what Nochlin already denounced in her essay Why Have There Been No Great Women Artists? these female artists are pioneers only according to the criteria of a canonical, male and patriarchal referential system.As a figure of the Belgian modernist movement, Simone Guillissen-Hoa (1916-1996) allows us, on one hand, to understand the specificities of the second modernist wave in post-war Europe and, on the other hand, to understand, through an intersectional reading of her identities and commitments, the gendered mechanisms in her practice, its reception and the construction of the history of architecture. Simone Guillissen-Hoa began her studies in architecture at the Institut Supérieur des Arts Décoratifs of La Cambre in 1935. She was the fourth female architect to graduate from the Brussels school and began her career during the early years of World War II in an economic context of scarcity of projects and in a binary and hierarchical gender system between design and architecture, female and male practitioners.Giving voice to networksThus, while Simone Guillissen-Hoa represents an inheritance and a model of empowerment, the analysis grids of individual and collective empowerment need to be specified. Indeed, we will be attentive to distance ourselves from the "mythology about artistic achievement", this “mysterious essence, rather like the golden nugget in Mrs. Grass’s chicken soup, called Genius or Talent”. If the reconstruction of the history of women architects and their work involves monographic research, it must also explore its limits and biases: the phenomenon of starification, the enunciation of a subject disconnected from its constellations, etc.At the edge of the canon, in tension between the monographic methodologies and collective portrait, this article proposes to weave several threads towards the specific and diversified tools, resources, and networks that Simone Guillissen-Hoa had to develop to claim her place at La Cambre, to follow the architectural curriculum, obtain a diploma and emerge professionally.Simone Guillissen-Hoa's constellationsWe want and we are looking for methodological and narrative tools that give voice to networks in order to think about a collective history of architecture and thus surpass the dominant canon. In a narrative polyphony, the mapping of networks, influences, actors, and relays - identified such as colleagues, family, friends, Simone Guillissen-Hoa's relationships, and inhabitants/users of the architect's achievements - offers an oral and expansive dimension to the official and conventional data preserved in the archives. Therefore, to destabilize hegemonic classifications and understand the nature and complexity of Simone Guillissen-Hoa's subjective constellations, three case studies will be developed: The role of male facilitators: the case of Alfred Roth; Ambivalence of associations with a male collaborator: the case of Jacques Dupuis; Architectural sisterhood: the fellows of the Union des Femmes Architectes de Belgique.info:eu-repo/semantics/inPres
Bruxelles gouvernée autrement ?Etude sur les aspirations des bruxellois
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Candidate ≠ Candidat. Quand les inégalités de genre entravent les candidates aux élections
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When Rural Meets Urban: Cultural Transfers Between Bohemia and Belgium 1870-1939
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Conclusions générales: Administration, R.G.P.D et secret des affaires :de la transparence à l'opacité ?
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Boundary Dissolution? The (Un)Making of Individual Boundaries in Sino-Congolese Couples Residing in Congo (DRC)
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Absence of gapless Majorana edge modes in few-leg bosonic flux ladders
No full textThe search for Majorana excitations has seen tremendous efforts in recent years, ultimately aiming for their individual controllability in future topological quantum computers. A promising framework to realize such exotic Majorana fermions are topologically ordered non-Abelian phases of matter, such as certain fractional quantum Hall states. Quantum simulators provide unprecedented controllability and versatility to investigate such states, and developing experimentally feasible schemes to realize and identify them is of immediate relevance. Motivated by recent experiments, we consider bosons on coupled chains, subjected to a magnetic flux and experiencing Hubbard repulsion. At magnetic filling factor ν = 1 ,similar systems on cylinders have been found to host the non-Abelian Moore-Read Pfaffian state in the bulk. Here, we address the question of whether more realistic few-leg ladders can host this exotic state and its chiral Majorana edge states. To this end, we perform extensive density-matrix renormalization-group simulations and determine the central charge of the ground state. While we do not find any evidence of gapless Majorana edge modes in systems of up to six legs, exact diagonalization of small systems reveals evidence for the Pfaffian state in the entanglement structure. By systematically varying the number of legs and monitoring the appearance and disappearance of this signal, our work highlights the importance of finite-size effects for the realization of exotic states in experimentally realistic systems. Published by the American Physical Society 2025SCOPUS: ar.jinfo:eu-repo/semantics/publishe